52.1.9 problem 7

Internal problem ID [8226]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 7
Date solved : Monday, January 27, 2025 at 03:46:27 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-y x&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 39

Order:=8; 
dsolve(diff(y(x),x$2)-x*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1+\frac {1}{6} x^{3}+\frac {1}{180} x^{6}\right ) y \left (0\right )+\left (x +\frac {1}{12} x^{4}+\frac {1}{504} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

AsymptoticDSolveValue[D[y[x],{x,2}]-x*y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_2 \left (\frac {x^7}{504}+\frac {x^4}{12}+x\right )+c_1 \left (\frac {x^6}{180}+\frac {x^3}{6}+1\right ) \]